Canonical Equilibria in Games with Flexible Information Acquisition

I study costly information acquisition by multiple decision-makers facing a strategic environment. First, each agent chooses an arbitrary \textit{signal} that provides information about an unknown state of nature. Each player incurs a cost that is increasing in the \textit{informativeness} of his signal. Then, once information has been acquired, agents choose their actions in a Bayesian game. I show that for every equilibrium, there exists an \textit{equivalent} pure strategy Bayes Nash equilibrium in which the space of signals is equal to the action space. The existence of such equilibrium, which I call \textit{canonical equilibrium}, provides a \textit{revelation principle} for games with flexible information acquisition. I also prove the existence of equilibrium, and I extend some results from single-agent costly information acquisition to strategic environments. Finally, through an example, I show that better information acquisition technology for all players can be detrimental to aggregate welfare